Some studies on finding the nearest volume-preserving matrix

摘要

Finding the nearest volume-preserving matrix for a given matrix is studied. A matrix equation is first obtained, which is a necessary condition for the solution to the problem. Then the equation is solved by the singular value decomposition method. Some additional results are also provided to further characterize the solution. Using these results, a numerical algorithm is introduced and a numerical test is given to illustrate the effectiveness of the algorithm.